Spatial autoregressive with a spatial autoregressive error term model and its parameter estimation with two-stage generalized spatial least square procedure

Abstract

Spatial relationship models often use dependence relationships into covariance structures through the autoregressive model. The autoregressive process is shown through the dependence relationship between a set of observations or a location from now on called the dependent spatial model. The Spatial dependent model is divided into two categories: spatial lag and spatial error. The spatial lag regression model is a model that considers dependent variables on an area with other areas associated with it, and the spatial error regression model is a model that takes into account the dependency of error values of an area with errors in other areas associated with it. Models with both dependencies are expressed as spatial autoregressive models with a spatial autoregressive error term (SAR-SAR). These dependencies resulted in the estimation of parameters by the ordinary least square method (OLS) resulting in inconsistent estimators. Therefore a special estimation method is required which results in a consistent estimate of the generalized spatial two-stage least square (GS2SLS). In this paper, we review the parameter estimation of SAR-SAR model with GS2SLS. To complete this paper, we also applicate of SAR-SAR model in dengue hemorrhagic fever (DHF) case in Surakarta, Central Java.